$ D = \left[\begin{array}{r}-1 \\ -2 \\ 0\end{array}\right]$ $ A = \left[\begin{array}{rr}3 & -2 \\ 0 & 3 \\ 0 & 4\end{array}\right]$ Is $ D A$ defined?
Solution: In order for multiplication of two matrices to be defined, the two inner dimensions must be equal. If the two matrices have dimensions $( m \times  n)$ and $( p \times q)$ , then $ n$ (number of columns in the first matrix) must equal $ p$ (number of rows in the second matrix) for their product to be defined. How many columns does the first matrix, $ D$ , have? How many rows does the second matrix, $ A$ , have? Since $ D$ has a different number of columns (1) than $ A$ has rows (3), $ D A$ is not defined.